// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gagan Goel <gagan.nith@gmail.com>
// Copyright (C) 2017 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_TRACE_H
#define EIGEN_CXX11_TENSOR_TENSOR_TRACE_H

namespace Eigen {

/** \class TensorTrace
  * \ingroup CXX11_Tensor_Module
  *
  * \brief Tensor Trace class.
  *
  *
  */

namespace internal {
    template <typename Dims, typename XprType> struct traits<TensorTraceOp<Dims, XprType>> : public traits<XprType>
    {
        typedef typename XprType::Scalar Scalar;
        typedef traits<XprType> XprTraits;
        typedef typename XprTraits::StorageKind StorageKind;
        typedef typename XprTraits::Index Index;
        typedef typename XprType::Nested Nested;
        typedef typename remove_reference<Nested>::type _Nested;
        static const int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;
        static const int Layout = XprTraits::Layout;
    };

    template <typename Dims, typename XprType> struct eval<TensorTraceOp<Dims, XprType>, Eigen::Dense>
    {
        typedef const TensorTraceOp<Dims, XprType>& type;
    };

    template <typename Dims, typename XprType> struct nested<TensorTraceOp<Dims, XprType>, 1, typename eval<TensorTraceOp<Dims, XprType>>::type>
    {
        typedef TensorTraceOp<Dims, XprType> type;
    };

}  // end namespace internal

template <typename Dims, typename XprType> class TensorTraceOp : public TensorBase<TensorTraceOp<Dims, XprType>>
{
public:
    typedef typename Eigen::internal::traits<TensorTraceOp>::Scalar Scalar;
    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
    typedef typename XprType::CoeffReturnType CoeffReturnType;
    typedef typename Eigen::internal::nested<TensorTraceOp>::type Nested;
    typedef typename Eigen::internal::traits<TensorTraceOp>::StorageKind StorageKind;
    typedef typename Eigen::internal::traits<TensorTraceOp>::Index Index;

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorTraceOp(const XprType& expr, const Dims& dims) : m_xpr(expr), m_dims(dims) {}

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dims& dims() const { return m_dims; }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename internal::remove_all<typename XprType::Nested>::type& expression() const { return m_xpr; }

protected:
    typename XprType::Nested m_xpr;
    const Dims m_dims;
};

// Eval as rvalue
template <typename Dims, typename ArgType, typename Device> struct TensorEvaluator<const TensorTraceOp<Dims, ArgType>, Device>
{
    typedef TensorTraceOp<Dims, ArgType> XprType;
    static const int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
    static const int NumReducedDims = internal::array_size<Dims>::value;
    static const int NumOutputDims = NumInputDims - NumReducedDims;
    typedef typename XprType::Index Index;
    typedef DSizes<Index, NumOutputDims> Dimensions;
    typedef typename XprType::Scalar Scalar;
    typedef typename XprType::CoeffReturnType CoeffReturnType;
    typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
    static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
    typedef StorageMemory<CoeffReturnType, Device> Storage;
    typedef typename Storage::Type EvaluatorPointerType;

    enum
    {
        IsAligned = false,
        PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
        BlockAccess = false,
        PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
        Layout = TensorEvaluator<ArgType, Device>::Layout,
        CoordAccess = false,
        RawAccess = false
    };

    //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
    typedef internal::TensorBlockNotImplemented TensorBlock;
    //===--------------------------------------------------------------------===//

    EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) : m_impl(op.expression(), device), m_traceDim(1), m_device(device)
    {
        EIGEN_STATIC_ASSERT((NumOutputDims >= 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
        EIGEN_STATIC_ASSERT((NumReducedDims >= 2) || ((NumReducedDims == 0) && (NumInputDims == 0)), YOU_MADE_A_PROGRAMMING_MISTAKE);

        for (int i = 0; i < NumInputDims; ++i) { m_reduced[i] = false; }

        const Dims& op_dims = op.dims();
        for (int i = 0; i < NumReducedDims; ++i)
        {
            eigen_assert(op_dims[i] >= 0);
            eigen_assert(op_dims[i] < NumInputDims);
            m_reduced[op_dims[i]] = true;
        }

        // All the dimensions should be distinct to compute the trace
        int num_distinct_reduce_dims = 0;
        for (int i = 0; i < NumInputDims; ++i)
        {
            if (m_reduced[i])
            {
                ++num_distinct_reduce_dims;
            }
        }

        eigen_assert(num_distinct_reduce_dims == NumReducedDims);

        // Compute the dimensions of the result.
        const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();

        int output_index = 0;
        int reduced_index = 0;
        for (int i = 0; i < NumInputDims; ++i)
        {
            if (m_reduced[i])
            {
                m_reducedDims[reduced_index] = input_dims[i];
                if (reduced_index > 0)
                {
                    // All the trace dimensions must have the same size
                    eigen_assert(m_reducedDims[0] == m_reducedDims[reduced_index]);
                }
                ++reduced_index;
            }
            else
            {
                m_dimensions[output_index] = input_dims[i];
                ++output_index;
            }
        }

        if (NumReducedDims != 0)
        {
            m_traceDim = m_reducedDims[0];
        }

        // Compute the output strides
        if (NumOutputDims > 0)
        {
            if (static_cast<int>(Layout) == static_cast<int>(ColMajor))
            {
                m_outputStrides[0] = 1;
                for (int i = 1; i < NumOutputDims; ++i) { m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1]; }
            }
            else
            {
                m_outputStrides.back() = 1;
                for (int i = NumOutputDims - 2; i >= 0; --i) { m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1]; }
            }
        }

        // Compute the input strides
        if (NumInputDims > 0)
        {
            array<Index, NumInputDims> input_strides;
            if (static_cast<int>(Layout) == static_cast<int>(ColMajor))
            {
                input_strides[0] = 1;
                for (int i = 1; i < NumInputDims; ++i) { input_strides[i] = input_strides[i - 1] * input_dims[i - 1]; }
            }
            else
            {
                input_strides.back() = 1;
                for (int i = NumInputDims - 2; i >= 0; --i) { input_strides[i] = input_strides[i + 1] * input_dims[i + 1]; }
            }

            output_index = 0;
            reduced_index = 0;
            for (int i = 0; i < NumInputDims; ++i)
            {
                if (m_reduced[i])
                {
                    m_reducedStrides[reduced_index] = input_strides[i];
                    ++reduced_index;
                }
                else
                {
                    m_preservedStrides[output_index] = input_strides[i];
                    ++output_index;
                }
            }
        }
    }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }

    EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/)
    {
        m_impl.evalSubExprsIfNeeded(NULL);
        return true;
    }

    EIGEN_STRONG_INLINE void cleanup() { m_impl.cleanup(); }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
    {
        // Initialize the result
        CoeffReturnType result = internal::cast<int, CoeffReturnType>(0);
        Index index_stride = 0;
        for (int i = 0; i < NumReducedDims; ++i) { index_stride += m_reducedStrides[i]; }

        // If trace is requested along all dimensions, starting index would be 0
        Index cur_index = 0;
        if (NumOutputDims != 0)
            cur_index = firstInput(index);
        for (Index i = 0; i < m_traceDim; ++i)
        {
            result += m_impl.coeff(cur_index);
            cur_index += index_stride;
        }

        return result;
    }

    template <int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
    {
        EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
        eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());

        EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
        for (int i = 0; i < PacketSize; ++i) { values[i] = coeff(index + i); }
        PacketReturnType result = internal::ploadt<PacketReturnType, LoadMode>(values);
        return result;
    }

#ifdef EIGEN_USE_SYCL
    // binding placeholder accessors to a command group handler for SYCL
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler& cgh) const { m_impl.bind(cgh); }
#endif

protected:
    // Given the output index, finds the first index in the input tensor used to compute the trace
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const
    {
        Index startInput = 0;
        if (static_cast<int>(Layout) == static_cast<int>(ColMajor))
        {
            for (int i = NumOutputDims - 1; i > 0; --i)
            {
                const Index idx = index / m_outputStrides[i];
                startInput += idx * m_preservedStrides[i];
                index -= idx * m_outputStrides[i];
            }
            startInput += index * m_preservedStrides[0];
        }
        else
        {
            for (int i = 0; i < NumOutputDims - 1; ++i)
            {
                const Index idx = index / m_outputStrides[i];
                startInput += idx * m_preservedStrides[i];
                index -= idx * m_outputStrides[i];
            }
            startInput += index * m_preservedStrides[NumOutputDims - 1];
        }
        return startInput;
    }

    Dimensions m_dimensions;
    TensorEvaluator<ArgType, Device> m_impl;
    // Initialize the size of the trace dimension
    Index m_traceDim;
    const Device EIGEN_DEVICE_REF m_device;
    array<bool, NumInputDims> m_reduced;
    array<Index, NumReducedDims> m_reducedDims;
    array<Index, NumOutputDims> m_outputStrides;
    array<Index, NumReducedDims> m_reducedStrides;
    array<Index, NumOutputDims> m_preservedStrides;
};

}  // End namespace Eigen

#endif  // EIGEN_CXX11_TENSOR_TENSOR_TRACE_H
